Open Access
2012 Alhazen's hyperbolic billiard problem
Nathan Poirier, Michael McDaniel
Involve 5(3): 273-282 (2012). DOI: 10.2140/involve.2012.5.273

Abstract

Given two points inside a circle in the hyperbolic plane, we study the problem of finding an isosceles triangle inscribed in the circle so that the two points belong to distinct congruent sides. By means of a reduction to the corresponding result in Euclidean geometry, we prove that this problem cannot generally be solved with hyperbolic ruler and compass.

Citation

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Nathan Poirier. Michael McDaniel. "Alhazen's hyperbolic billiard problem." Involve 5 (3) 273 - 282, 2012. https://doi.org/10.2140/involve.2012.5.273

Information

Received: 18 January 2011; Revised: 24 June 2011; Accepted: 26 June 2011; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1273.51012
MathSciNet: MR3044613
Digital Object Identifier: 10.2140/involve.2012.5.273

Subjects:
Primary: 51M04 , 51M10 , 51M15
Secondary: 51M09

Keywords: Alhazen , hyperbolic geometry

Rights: Copyright © 2012 Mathematical Sciences Publishers

Vol.5 • No. 3 • 2012
MSP
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